Interaction force in a vertical dust chain inside a glass box

Small number dust particle clusters can be used as probes for plasma diagnostics. The number of dust particles as well as cluster size and shape can be easily controlled employing a glass box placed within a Gaseous Electronics Conference (GEC) rf reference chamber to provide confinement of the dust. The plasma parameters inside this box and within the larger plasma chamber have not yet been adequately defined. Adjusting the rf power alters the plasma conditions causing structural changes of the cluster. This effect can be used to probe the relationship between the rf power and other plasma parameters. This experiment employs the sloshing and breathing modes of small cluster oscillations to examine the relationship between system rf power and the particle charge and plasma screening length inside the glass box. The experimental results provided indicate that both the screening length and dust charge decrease as rf power inside the box increases. The decrease in dust charge as power increases may indicate that ion trapping plays a significant role in the sheath.

Figure 1

Experimental setup. The open-ended glass box shown here has dimensions of 12 mm × 10.5 mm (height × width). Dust particle oscillation was generated through modulation of an external dc bias introduced on the lower electrode.

Figure 2

Top and side views of helical structures formed from particle cluster at varying rf powers using the technique described in the text. In all cases, the background pressure is held at 20 Pa. (a) One-dimensional (1D)single chain, rf power 1.23 W. (b) Two-dimensional (2D) zigzag structure, rf power 1.27 W. (c) Three-dimensional (3D) three-chain helical structure, rf power 1.32 W. (d) 3D four-chain helical structure, rf power 1.39 W. (e) 3D five-chain helical structure, rf power 1.80 W. Due to the width of the laser sheet used for illumination and the specific portion of the chain imaged by the camera, not every particle in each structure is visible in these side view images. As stated above, a two-particle vertical chain was chosen to test the validity of Eqs. (3) and (4), due to its stable structure during forced oscillation under different rf powers. Figure 3 shows the relative vertical positions and interparticle separations for such a two-particle chain under various rf powers.

Figure 3

Vertical height and interparticle separation variations for a two-particle chain under various rf powers. From (a) to (e) the corresponding rf powers are 1.23, 1.27, 1.32, 1.39, and 1.80 W, respectively. These power settings are identical to those used for transitioning from a single-chain through a five-chain structure when ten particles are confined within the glass box (Fig. 2). The bright region in the lower part of the figure is the lower powered electrode, and the glass box top edge can be seen in the upper part of the figure.

Figure 4

(a) Frequency response data for vertically driven oscillation data for a two-particle chain at a rf power of 1.23 W. Symbols represent experimental data while lines represent the theoretical fit as explained in the text. Breathing and sloshing modes are fitted by solid and dotted lines, respectively. (b) Mode analysis showing the same values for sloshing and breathing oscillation frequencies as derived from the driven oscillation method. The four modes shown are the (1) horizontal relative, (2) vertical sloshing, (3) horizontal sloshing, and (4) vertical breathing modes.

Figure 5

(a) Breathing and sloshing frequencies, (b) the square of the ratio of the breathing to sloshing frequency as a function of the rf power, and (c) the equilibrium separation distance between the two particles as a function of the rf power. Solid lines are included to guide the eye.

Figure 6

Small clusters with (a) six particles at 1.69 W, (b) nine particles at 1.47 W, and (c) 12 particles at 1.36 W. The scale is for both horizontal and vertical.

Figure 7

Experimental result of the screening parameter as a function of the rf power.

Figure 8

(a) Absolute value of dust charge, and (b) ratio of the linear force constant $K_0$ to $m_d{\omega }_{sl}^2$ as a function of the rf power. Fit lines serve to guide the eye.